Fig. 1. Structure diagram of frequency-locked circuit

Fig. 2. Flow chart of the auto-relock process

Fig. 3. Circuit pure proportional gain bandwidth

Fig. 4. Allen deviation of the error signal before and after the locking of the frequency-locked circuit

Fig. 5. Schematic diagram of structure of ultra-stable laser system

Fig. 6. Result of auto-relock

Fig. 7. Result diagram of beat frequency. (a) Variation in beat frequency with time with the linear drift of 12.4 mHz/s removed; (b) Allan deviation of the beat frequency calculated with data in (a)